1. Field of the Invention
The present invention relates to a method for generating atomic coordinates required upon performing material simulation.
2. Description of the Related Art
For performing material simulation by molecular dynamics, molecular orbital methods and so forth, an initial arrangement of all objective crystal atoms is necessary. A crystal model is defined by designating all coordinates of the atoms that are included in the crystal. Particularly, when the crystal includes a grain boundary, it is required to arrange each crystal grain with tilting at a certain angle to form a desired grain boundary. Conventionally, an atomic coordinate generating method of this kind has been disclosed in Surface Science, Vol. 31, (1972), pp. 138 to 160. Necessary crystal grains are prepared per surface orientations and are rotated around the surface normal to form a symmetric grain boundary that is a mirror surface to prepare a replica of atom at a reversed image position.
In the prior art set forth above, generation methods of atom positions per surface orientation must be prepared. Therefore, surface orientation generating means have to be prepared for required surface orientations. Also, since the prepared means are differentiated per surface orientation, the program becomes complicated. Furthermore, since the rotated crystal must be cut off to make a basic cell, an extra temporary storage region is required.
A first object of the present invention is to prepare a method and a system for generating atomic coordinates which can easily and efficiently perform generation of coordinate data of model atoms forming a crystal body having a designated surface orientation.
A second object of the present invention is to provide a method and a system for generating atomic coordinates to avoid formation of any xe2x80x9cdefectxe2x80x9d in the prepared crystal model.
A third object of the present invention is to provide a method and a system for generating atomic coordinates which can restrict a storage region to be used in a small range.
According to the first aspect of the invention, an atomic coordinates generating method that generates atomic coordinate positions within a rectangular parallelepiped as an outer frame of a crystal having a predetermined plane orientation is provided, comprising:
(1) step of deriving a sphere circumscribing said rectangular parallelepiped, (2) step of deriving a cubic circumscribing said sphere, (3) step of generating atomic coordinates within said cubic, (4) step of providing rotation for the generated atomic coordinates for matching a bottom of said cubic with said plane orientation, and (5) step of checking whether the atomic coordinates after rotation is present within a rectangular parallelepiped having said predetermined plane orientation, and selecting only coordinates present within said rectangular parallelepiped.
In the preferred construction, said atomic coordinates generating step comprises (a) step of deriving a repetition number of a unit crystal in each crystal axis direction, and (b) step of generating the atomic position coordinates on the basis of said repetition number and an atom position within a unit cell.
In another preferred construction, said atomic coordinates generating step comprises (a) step of deriving a repetition number of a unit cell in each crystal axis direction, and (b) step of generating the atomic position coordinates on the basis of said repetition number and atom positions within a unit cell,
steps from (b) to (5) are repeated for all atomic coordinates within said cubic.
In another preferred construction, respective edges of said cubic are parallel to x, y and z axes of orthogonal coordinates and (001) plane of crystal included in said rectangular parallelepiped is parallel to an x-y plane of said orthogonal coordinates.
In another preferred construction, respective edges of said cubic are parallel to x, y and z axes of orthogonal coordinates and (001) plane of crystal included in said rectangular parallelepiped is parallel to an x-y plane of said orthogonal coordinates,
in advance of said step (4), a rotational transformation matrix being obtained beforehand for placing said plane orientation in parallel with said x-y plane.
According to the second aspect of the invention, an atomic coordinates generating system generating an atomic coordinate position within a rectangular parallelepiped as an outer frame of a crystal having a predetermined plane orientation, comprises
means for inputting a crystal size, a lattice constant, relative atom positions in the unit cell and a Miller indices as parameters,
position generating means, and region calculating means for deriving a sphere circumscribing said rectangular parallelepiped from said crystal size, deriving a size of a cubic circumscribing said sphere, and deriving repetition number of unit cell on the basis of the size of said cubic and said lattice constant, as a position generating region,
atomic position generating means for generating the unit cell within said position generating region and generating atom coordinates according to said relative atom positions in the unit cell,
rotational transformation means for providing rotation for matching a bottom of said cubic with said plane orientation with respect to derived atomic coordinates, and
region judgment means for checking whether the atom coordinates after rotation are present within the rectangular parallelepiped having said predetermined plane orientation and selecting only atom coordinates presenting within said rectangular parallelepiped.
In the preferred construction, respective edges of said cubic are parallel to x, y and z axes of orthogonal coordinates and (001) plane of crystal included in said rectangular parallelepiped is parallel to an x-y plane of said orthogonal coordinates,
said system further comprises means for obtaining beforehand a rotational transformation matrix for placing said plane orientation in parallel with said x-y plane in advance of process by said rotational transformation means.
In another preferred construction, a process of generation of atomic coordinates by said atomic position generating means to selection by said region judgment means is repeated for all atomic coordinates within said cubic.
According to another aspect of the invention, a computer readable memory storing atomic coordinates generating program generating atomic coordinate positions within a rectangular parallelepiped as an outer frame of having a predetermined plane orientation, as loaded and executed by a computer, said atomic coordinates generating program comprises (1) step of deriving a sphere circumscribing said rectangular parallelepiped, (2) step of deriving a cubic circumscribing said sphere, (3)
step of generating atomic coordinates within said cubic, (4) step of providing rotation for the generated atomic coordinates for matching a bottom of said cubic with said plane orientation, and (5) step of checking whether the atomic coordinates after rotation are present within a rectangular parallelepiped having said predetermined plane orientation, and selecting only coordinates present within said rectangular parallelepiped.
Further objects, features and effects of the present invention will become apparent from the detailed description given hereinafter.